For a quantitative measure, the system was trained as usual on the
interaction between the two individuals and learned the usual
predictive mapping
.
Since real-time is not an
issue for this kind of test, the system was actually permitted to use
more Gaussian models and more dimensions to learn
.

Once trained on a portion of the data, the system's ability to perform
prediction was tested on the remainder of the sequence. Once again,
the pdf allows us to compute an estimated
for any
given
short term memory. The expectation was used to predict
and not the arg max since it is the least squares
estimator. The prediction was then compared to the true result in the future of the time series and RMS errors were
computed. Of course, the system only observed the immediate past
reaction of both user A and user B which is contained in .
Thus, the values
are effectively
being used to compute
.
In addition, the system is
predicting the immediate reaction of both users
(A and B) in the whole
vector. For comparison, RMS errors
are shown against the nearest neighbour and
constant velocity estimates. The nearest neighbour estimate merely
assumes that
and the constant velocity
assumes that
.

Table 9.2:
RMS Errors

Nearest Neighbour

Constant Velocity

ARL

1.57 %

0.85 %

0.62 %

Table 9.2 depicts the RMS errors on the test interaction and
these suggest that the system is a better instantaneous predictor than
the above two methods. Therefore, it should be useful as a Kalman
filter-type of predictor for helping tracking systems.